MathDB
Turkey NMO 2007 1st Round - P19 (Algebra)

Source:

October 4, 2012
AMCAIMEAIME II

Problem Statement

If x1=5,x2=401x_1=5, x_2=401, and xn=xn21xn1 x_n=x_{n-2}-\frac 1{x_{n-1}} for every 3nm3\leq n \leq m, what is the largest value of mm?
<spanclass=latexbold>(A)</span> 406<spanclass=latexbold>(B)</span> 2005<spanclass=latexbold>(C)</span> 2006<spanclass=latexbold>(D)</span> 2007<spanclass=latexbold>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 406 \qquad<span class='latex-bold'>(B)</span>\ 2005 \qquad<span class='latex-bold'>(C)</span>\ 2006 \qquad<span class='latex-bold'>(D)</span>\ 2007 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}